SRC/ssycon_3.f(3)          Library Functions Manual          SRC/ssycon_3.f(3)

NAME
       SRC/ssycon_3.f

SYNOPSIS
   Functions/Subroutines
       subroutine ssycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work,
           iwork, info)
           SSYCON_3

Function/Subroutine Documentation
   subroutine ssycon_3 (character uplo, integer n, real, dimension( lda, * )
       a, integer lda, real, dimension( * ) e, integer, dimension( * ) ipiv,
       real anorm, real rcond, real, dimension( * ) work, integer, dimension(
       * ) iwork, integer info)
       SSYCON_3

       Purpose:


           !> SSYCON_3 estimates the reciprocal of the condition number (in the
           !> 1-norm) of a real symmetric matrix A using the factorization
           !> computed by DSYTRF_RK or DSYTRF_BK:
           !>
           !>    A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),
           !>
           !> where U (or L) is unit upper (or lower) triangular matrix,
           !> U**T (or L**T) is the transpose of U (or L), P is a permutation
           !> matrix, P**T is the transpose of P, and D is symmetric and block
           !> diagonal with 1-by-1 and 2-by-2 diagonal blocks.
           !>
           !> An estimate is obtained for norm(inv(A)), and the reciprocal of the
           !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
           !> This routine uses BLAS3 solver SSYTRS_3.
           !>

       Parameters
           UPLO

           !>          UPLO is CHARACTER*1
           !>          Specifies whether the details of the factorization are
           !>          stored as an upper or lower triangular matrix:
           !>          = 'U':  Upper triangular, form is A = P*U*D*(U**T)*(P**T);
           !>          = 'L':  Lower triangular, form is A = P*L*D*(L**T)*(P**T).
           !>

           N

           !>          N is INTEGER
           !>          The order of the matrix A.  N >= 0.
           !>

           A

           !>          A is REAL array, dimension (LDA,N)
           !>          Diagonal of the block diagonal matrix D and factors U or L
           !>          as computed by SSYTRF_RK and SSYTRF_BK:
           !>            a) ONLY diagonal elements of the symmetric block diagonal
           !>               matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
           !>               (superdiagonal (or subdiagonal) elements of D
           !>                should be provided on entry in array E), and
           !>            b) If UPLO = 'U': factor U in the superdiagonal part of A.
           !>               If UPLO = 'L': factor L in the subdiagonal part of A.
           !>

           LDA

           !>          LDA is INTEGER
           !>          The leading dimension of the array A.  LDA >= max(1,N).
           !>

           E

           !>          E is REAL array, dimension (N)
           !>          On entry, contains the superdiagonal (or subdiagonal)
           !>          elements of the symmetric block diagonal matrix D
           !>          with 1-by-1 or 2-by-2 diagonal blocks, where
           !>          If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
           !>          If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
           !>
           !>          NOTE: For 1-by-1 diagonal block D(k), where
           !>          1 <= k <= N, the element E(k) is not referenced in both
           !>          UPLO = 'U' or UPLO = 'L' cases.
           !>

           IPIV

           !>          IPIV is INTEGER array, dimension (N)
           !>          Details of the interchanges and the block structure of D
           !>          as determined by SSYTRF_RK or SSYTRF_BK.
           !>

           ANORM

           !>          ANORM is REAL
           !>          The 1-norm of the original matrix A.
           !>

           RCOND

           !>          RCOND is REAL
           !>          The reciprocal of the condition number of the matrix A,
           !>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
           !>          estimate of the 1-norm of inv(A) computed in this routine.
           !>

           WORK

           !>          WORK is REAL array, dimension (2*N)
           !>

           IWORK

           !>          IWORK is INTEGER array, dimension (N)
           !>

           INFO

           !>          INFO is INTEGER
           !>          = 0:  successful exit
           !>          < 0:  if INFO = -i, the i-th argument had an illegal value
           !>

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Contributors:


           !>
           !>  June 2017,  Igor Kozachenko,
           !>                  Computer Science Division,
           !>                  University of California, Berkeley
           !>
           !>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
           !>                  School of Mathematics,
           !>                  University of Manchester
           !>
           !>

       Definition at line 169 of file ssycon_3.f.

Author
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LAPACK                          Version 3.12.0               SRC/ssycon_3.f(3)